If you are going to shoot short clips 10-120 seconds at a time in 4K, you should be fine at least for several clips. For indoors, if you are planning to shoot long pieces, you should still keep in mind that internal overheating may occur, even if the camera is not exposed to sun rays.
There are few tricks you can use to minimize overheating:
1) keep the battery door and the flash door open
2) leave the LCD screen away from the camera body
3) try using external batteries – it can be very helpful. For a6500 you can literally use a USB power bank that people buy to charge smartphones.